Two criteria for locally noetherian Grothendieck categories

被引：0
|
作者：
Banerjee, Abhishek [1 ]
机构：
[1] Indian Inst Sci, Dept Math, Bangalore, India
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 2023年 / 227卷 / 03期
关键词：
Finitely injective objects; Local summands; Chain conditions; Grothendieck categories; INDECOMPOSABLE DECOMPOSITIONS; DIRECT SUMS; RINGS; MODULES; THEOREM;
D O I：
10.1016/j.jpaa.2022.107233
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give two criteria for a Grothendieck category to be locally noetherian. The first of these is in terms of direct sum decompositions into uniform components. The second is related to the existence of finitely injective objects that cannot be expressed as a direct sum of injectives.
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